A cold front will move slowly through Texas and Oklahoma. As it presses further east, the circulation around an upper high (orange arrows on map) will contribute to the front stalling. Or, at least moving with only a turtle’s pace.

Second, moisture-charged air flowing unimpeded from the Gulf will provide a strong over-running environment.

Finally, a series of weak waves are expected to move along in the jet stream flow (blue arrows).

These ingredients spell "heavy rainfall" in the 2-4" range during the 4-day period. A faster frontal movement would lower these rainfall amounts. I am going with the slower progression based on the upper pattern.

So periods of rain and thunderstorms are in my forecast Thursday-Sunday.

The front should eventually move through as the upper high weakens. This would provide a more stable pattern by early next week.

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